Highway Capacity Manual 2010 - Volume 4 | 2010 Highway ...hcm2010.org/system/datas/112/original/January-July 2012 page... · Highway Capacity Manual 2010 Methodology Page 11-16 Chapter

Highway Capacity Manual 2010

Methodology Page 11-16 Chapter 11/Basic Freeway Segments January 2012

The length of the grade is generally taken from a highway profile. It typically

includes the straight portion of the grade plus some portion of the vertical curves

at the beginning and end of the grade. It is recommended that 25% of the length

of the vertical curves at both ends of the grade be included in the length. Where

two consecutive upgrades are present, 50% of the length of the vertical curve

joining them is included in the length of each grade.

In the analysis of upgrades, the point of interest is generally at the end of the

grade, where heavy vehicles would have the maximum effect on operations.

However, if a ramp junction is being analyzed, for example, the length of the

grade to the merge or diverge point would be used.

On composite grades, the relative steepness of segments is important. If a 5%

upgrade is followed by a 2% upgrade, for example, the maximum impact of

heavy vehicles is most likely at the end of the 5% segment. Heavy vehicles would

be expected to accelerate after entering the 2% segment.

Upgrade (%)

Length (mi)

Proportion of Trucks and Buses 2% 4% 5% 6% 8% 10% 15% 20% ≥25%

≤2 All 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

>2–3

0.00–0.25 >0.25–0.50 >0.50–0.75 >0.75–1.00 >1.00–1.50

>1.50

1.5 1.5 1.5 2.0 2.5 3.0

1.5 1.5 1.5 2.0 2.5 3.0

1.5 1.5 1.5 2.0 2.5 2.5

1.5 1.5 1.5 2.0 2.5 2.5

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

>3–4

0.00–0.25 >0.25–0.50 >0.50–0.75 >0.75–1.00 >1.00–1.50

>1.50

1.5 2.0 2.5 3.0 3.5 4.0

1.5 2.0 2.5 3.0 3.5 3.5

1.5 2.0 2.0 2.5 3.0 3.0

1.5 2.0 2.0 2.5 3.0 3.0

1.5 2.0 2.0 2.5 3.0 3.0

1.5 2.0 2.0 2.5 3.0 3.0

1.5 1.5 2.0 2.0 2.5 2.5

1.5 1.5 2.0 2.0 2.5 2.5

1.5 1.5 2.0 2.0 2.5 2.5

>4–5

0.00–0.25 >0.25–0.50 >0.50–0.75 >0.75–1.00

>1.00

1.5 3.0 3.5 4.0 5.0

1.5 2.5 3.0 3.5 4.0

1.5 2.5 3.0 3.5 4.0

1.5 2.5 3.0 3.5 4.0

1.5 2.0 2.5 3.0 3.5

1.5 2.0 2.5 3.0 3.5

1.5 2.0 2.5 3.0 3.0

1.5 2.0 2.5 3.0 3.0

1.5 2.0 2.5 3.0 3.0

>5–6

0.00–0.25 >0.25–0.30 >0.30–0.50 >0.50–0.75 >0.75–1.00

>1.00

2.0 4.0 4.5 5.0 5.5 6.0

2.0 3.0 4.0 4.5 5.0 5.0

1.5 2.5 3.5 4.0 4.5 5.0

1.5 2.5 3.0 3.5 4.0 4.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

>6

0.00–0.25 >0.25–0.30 >0.30–0.50 >0.50–0.75 >0.75–1.00

>1.00

4.0 4.5 5.0 5.5 6.0 7.0

3.0 4.0 4.5 5.0 5.5 6.0

2.5 3.5 4.0 4.5 5.0 5.5

2.5 3.5 4.0 4.5 5.0 5.5

2.5 3.5 3.5 4.0 4.5 5.0

2.5 3.0 3.0 3.5 4.0 4.5

2.0 2.5 2.5 3.0 3.5 4.0

2.0 2.5 2.5 3.0 3.5 4.0

2.0 2.5 2.5 3.0 3.5 4.0

Note: Interpolation for percentage of trucks and buses is recommended to the nearest 0.1.

The grade length should include 25% of the length of the vertical curves at the start and end of the grade.

With two consecutive upgrades, 50% of the length of the vertical curve joining them should be included.

The point of interest is usually the spot where heavy vehicles would have the greatest impact on operations: the top of a grade, the top of the steepest grade in a series, or a ramp junction, for example.

Exhibit 11-11 PCEs for Trucks and Buses

(ET) on Upgrades


Chapter 12/Freeway Weaving Segments Page 12-25 Applications July 2012

4. APPLICATIONS

The methodology of this chapter is most often used to estimate the capacity

and LOS of freeway weaving segments. The steps are most easily applied in the

operational analysis mode, that is, all traffic and roadway conditions are

specified, and a solution for the capacity (and v/c ratio) is found along with an

expected LOS. Other types of analysis, however, are possible.

DEFAULT VALUES

An NCHRP report (10) provides a comprehensive presentation of potential

default values for uninterrupted-flow facilities. Default values for freeways are

summarized in Chapter 11, Basic Freeway Segments. These defaults cover the

key characteristics of PHF and percentage of heavy vehicles. Recommendations

are based on geographical region, population, and time of day. All general

freeway default values may be applied to the analysis of weaving segments in

the absence of field data or projected conditions.

There are many specific variables related to weaving segments. It is,

therefore, virtually impossible to specify default values of such characteristics as

length, width, configuration, and balance of weaving and nonweaving flows.

Weaving segments are a detail of the freeway design and should therefore be

treated only with the specific characteristics of the segment known or projected.

Small changes in some of these variables can and do yield significant changes in

the analysis results.

TYPES OF ANALYSIS

The methodology of this chapter can be used in three types of analysis:

operational, design, and planning and preliminary engineering.

Operational Analysis

The methodology of this chapter is most easily applied in the operational

analysis mode. In this application, all weaving demands and geometric

characteristics are known, and the output of the analysis is the expected LOS and

the capacity of the segment. Secondary outputs include the average speed of

component flows, the overall density in the segment, and measures of lane-

changing activity.

Design Analysis

In design applications, the desired output is the length, width, and

configuration of a weaving segment that will sustain a target LOS for given

demand flows. This application is best accomplished by iterative operational

analyses on a small number of candidate designs.

Generally, there is not a great deal of flexibility in establishing the length and

width of a segment, and only limited flexibility in potential configurations. The

location of intersecting facilities places logical limitations on the length of the

weaving segment. The number of entry and exit lanes on ramps and the freeway

itself limits the number of lanes to, at most, two choices. The entry and exit

Design analysis is best accomplished by iterative operational analyses on a small number of candidate designs.


Methodology Page 13-14 Chapter 13/Freeway Merge and Diverge Segments July 2012

maneuver. Thus, for off-ramps, the flow in Lanes 1 and 2 consists of all off-ramp

vehicles and a proportion of freeway through vehicles, as in Equation 13-8:

FDRFR Pvvvv 12

where

v12 = flow rate in Lanes 1 and 2 of the freeway immediately upstream of the

deceleration lane (pc/h),

vR = flow rate on the off-ramp (pc/h), and

PFD = proportion of through freeway traffic remaining in Lanes 1 and 2

immediately upstream of the deceleration lane.

For off-ramps, the point at which flows are defined is the beginning of the

deceleration lane(s), regardless of whether this point is within or outside the

ramp influence area.

Exhibit 13-7 contains the equations used to estimate PFD at off-ramp diverge

areas. As was the case for on-ramps (merge areas), the value of PFD for four-lane

freeways is trivial, since only Lanes 1 and 2 exist.

No. of Freeway Lanesa Model(s) for Determining PFD

4 000.1FDP

6

RFFD vvP 000046.0000025.0760.0

UP/604.0000039.0717.0 LvvP UFFD when vU/LUP ≤ 0.2b

DOWN/124.0000021.0616.0 LvvP DFFD

8 436.0FDP

SELECTING EQUATIONS FOR PFD FOR SIX-LANE FREEWAYS

Adjacent Upstream

Ramp Subject Ramp

Adjacent Downstream

Ramp Equation(s) Used

None None None On Off On On Off Off

Off Off Off Off Off Off Off Off Off

None On Off

None None On Off On Off

Equation 13-9 Equation 13-9 Equation 13-11 or 13-9 Equation 13-10 or 13-9 Equation 13-9 Equation 13-10 or 13-9 Equation 13-11, 13-10, or 13-9 Equation 13-9 Equation 13-11 or 13-9

Note: a 4 lanes = two lanes in each direction; 6 lanes = three lanes in each direction; 8 lanes = four lanes in each direction. b When vU/LUP > 0.2, use Equation 13-9. If an adjacent ramp on a six-lane freeway is not a one-lane, right-side off-ramp, use Equation 13-9.

For six-lane freeways, three equations are presented. Equation 13-9 is the

base case for isolated ramps or for cases in which the impact of adjacent ramps

can be ignored. Equation 13-10 addresses cases in which there is an adjacent

upstream on-ramp, while Equation 13-11 addresses cases in which there is an

adjacent downstream off-ramp. Adjacent upstream off-ramps and downstream

on-ramps have not been found to have a statistically significant impact on

diverge operations and may be ignored. All variables in Exhibit 13-7 are as

previously defined.

Equation 13-8

Exhibit 13-7 Models for Predicting PFD at Off-Ramps or Diverge Areas

Equation 13-9

Equation 13-10

Equation 13-11


Chapter 13/Freeway Merge and Diverge Segments Page 13-15 Methodology July 2012

Insufficient information is available to establish an impact of adjacent ramps

on eight-lane freeways (four lanes in each direction). This methodology does not

include such an impact.

Where an adjacent upstream on-ramp or downstream off-ramp on a six-lane

freeway exists, a determination as to whether the ramp is close enough to the

subject off-ramp to affect its operation is necessary. As was the case for on-

ramps, this is done by finding the equilibrium distance LEQ. This distance is

determined when Equation 13-9 yields the same value of PFD as Equation 13-10

(for adjacent upstream on-ramps) or Equation 13-11 (adjacent downstream off-

ramps). When the actual distance between ramps is greater than or equal to LEQ,

Equation 13-9 is used. When the actual distance between ramps is less than LEQ,

Equation 13-10 or Equation 13-11 is used as appropriate.

For adjacent upstream on-ramps, use Equation 13-12 to find the equilibrium

distance:

RF

uEQ

vv

vL

000076.0000023.0071.0

For adjacent downstream off-ramps, use Equation 13-13:

RF

DEQ

vv

vL

000369.0000032.015.1

where all terms are as previously defined.

In cases where Equation 13-12 indicates that Equation 13-10 should be used

to determine PFD, but vU/LUP > 0.20, Equation 13-9 must be used as a default. This

is due to the valid calibration range of Equation 13-10, and the fact that it will

yield unreasonable results when vU/LUP exceeds 0.20. This will lead to step-

function changes in PFD for values just below or above vU/LUP = 0.20.

A special case exists when both an adjacent upstream on-ramp and an

adjacent downstream off-ramp are present. In such cases, two solutions for PFD may arise, depending on which adjacent ramp is considered (both ramps cannot

be considered simultaneously). In such cases, the larger value of PFD is used.

As was the case for merge areas, the algorithms used to include the impact of

an upstream or downstream ramp on a six-lane freeway are only valid for single-

lane, right-side adjacent ramps. Where adjacent ramps consist of two-lane

junctions or major diverge configurations, or where they are on the left side of

the freeway, Equation 13-9 is always applied.

Checking the Reasonableness of the Lane Distribution Prediction

The algorithms of Exhibit 13-6 and Exhibit 13-7 were developed through

regression analysis of a large database. Unfortunately, regression-based models

may yield unreasonable or unexpected results when applied outside the strict

limits of the calibration database, and they may have inconsistencies at their

boundaries.

Therefore, it is necessary to apply some limits to predicted values of flow in

Lanes 1 and 2 (v12). The following limitations apply to all such predictions:

Equation 13-12

Equation 13-13

When both an adjacent upstream on-ramp and an adjacent downstream off-ramp are present, the larger resulting value of PFD is used.

When an adjacent ramp to a diverge area on a six-lane freeway is not a one-lane, right-side ramp, apply Equation 13-9.

Reasonableness checks on the value of v12.


Methodology Page 13-16 Chapter 13/Freeway Merge and Diverge Segments July 2012

1. The average flow per lane in the outer lanes of the freeway (lanes other

than 1 and 2) should not be higher than 2,700 pc/h/ln.

2. The average flow per lane in outer lanes should not be higher than 1.5

times the average flow in Lanes 1 and 2.

These limits guard against cases in which the predicted value of v12 implies

an unreasonably high flow rate in outer lanes of the freeway. When either of

these limits is violated, an adjusted value of v12 must be computed and used in

the remainder of the methodology.

Application to Six-Lane Freeways

On a six-lane freeway (three lanes in one direction), there is only one outer

lane to consider. The flow rate in this outer lane (Lane 3) is given by Equation 13-

14:

123 vvv F

where

v3 = flow rate in Lane 3 of the freeway (pc/h/ln),

vF = flow rate on freeway immediately upstream of the ramp influence area

(pc/h), and

v12 = flow rate in Lanes 1 and 2 immediately upstream of the ramp influence

area (pc/h).

Then, if v3 is greater than 2,700 pc/h, use Equation 13-15:

700,212 Fa vv

If v3 is greater than 1.5 × (v12/2), use Equation 13-16:

75.112

Fa

vv

where v12a equals the adjusted flow rate in Lanes 1 and 2 immediately upstream

of the ramp influence area (pc/h) and all other variables are as previously

defined.

In cases where both limitations on outer lane flow rate are violated, the result

yielding the highest value of v12a is used. The adjusted value replaces the original

value of v12 and the analysis continues.

Application to Eight-Lane Freeways

On eight-lane freeways, there are two outer lanes (Lanes 3 and 4). Thus, the

limiting values cited previously apply to the average flow rate per lane in these

lanes. The average flow in these lanes is computed from Equation 13-17:

212

34

vvv F

av

where vav34 equals the flow rate in outer lanes (pc/h/ln) and all other variables are

as previously defined.

Then, if vav34 is greater than 2,700, use Equation 13-18:

400,512 Fa vv

Equation 13-14

Equation 13-15

Equation 13-16

Equation 13-17

Equation 13-18


Chapter 13/Freeway Merge and Diverge Segments Page 13-17 Methodology July 2012

If vav34

is greater than 1.5 × (v12

/2), use Equation 13-19:

50.212

Fa

vv

where all terms are as previously defined.

In cases where both limitations on outer lane flow rate are violated, the result

yielding the highest value of v12a is used. The adjusted value replaces the original

value of v12 and the analysis continues.

Summary of Step 2

At this point, an appropriate value of v12 has been computed and adjusted as

necessary.

Step 3: Estimate the Capacity of the Ramp–Freeway Junction and

Compare with Demand Flow Rates

There are three major checkpoints for the capacity of a ramp–freeway

junction:

1. The capacity of the freeway immediately downstream of an on-ramp or

immediately upstream of an off-ramp,

2. The capacity of the ramp roadway, and

3. The maximum flow rate entering the ramp influence area.

In most cases, the freeway capacity is the controlling factor. Studies (1) have

shown that the turbulence in the vicinity of a ramp–freeway junction does not

diminish the capacity of the freeway.

The capacity of the ramp roadway is rarely a factor at on-ramps, but it can

play a major role at off-ramp (diverge) junctions. Failure of a diverge junction is

most often caused by a capacity deficiency on the off-ramp roadway or at its

ramp–street terminal.

While this methodology establishes a maximum desirable rate of flow

entering the ramp influence area, exceeding this value does not cause a failure.

Instead, it means that operations may be less desirable than indicated by the

methodology. At off-ramps, the total flow rate entering the ramp influence area

is merely the estimated value of v12. At on-ramps, however, the on-ramp flow

also enters the ramp influence area. Therefore, the total flow entering the ramp

influence area at an on-ramp is given by Equation 13-20:

RR vvv 1212

where vR12 is the total flow rate entering the ramp influence area at an on-ramp

(pc/h) and all other variables are as previously defined.

Exhibit 13-8 shows capacity values for ramp–freeway junctions. Exhibit 13-9

shows similar values for high-speed ramps on multilane highways and C-D

roadways within freeway interchanges. Exhibit 13-10 shows the capacity of ramp

roadways.

Equation 13-19

Locations for checking the capacity of a ramp–freeway junction.

Freeway capacity immediately downstream of an on-ramp or upstream of an off-ramp is usually the controlling capacity factor.

Failure of a diverge junction is usually caused by a capacity deficiency at the ramp–street terminal or on the off-ramp roadway.

Equation 13-20


Methodology Page 14-16 Chapter 14/Multilane Highways January 2012

cars. The aggregate impact of heavy vehicles on the traffic stream, however,

increases as the number and percentage of heavy vehicles increase.

Percent Upgrade

Length (mi)

Proportion of Trucks and Buses 2% 4% 5% 6% 8% 10% 15% 20% 25%

≤2 All 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

>2 – 3

0.00 – 0.25 >0.25 – 0.50 >0.50 – 0.75 >0.75 – 1.00 >1.00 – 1.50

>1.50

1.5 1.5 1.5 2.0 2.5 3.0

1.5 1.5 1.5 2.0 2.5 3.0

1.5 1.5 1.5 2.0 2.5 2.5

1.5 1.5 1.5 2.0 2.5 2.5

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

1.5 1.5 1.5 1.5 2.0 2.0

>3 – 4

0.00 – 0.25 >0.25 – 0.50 >0.50 – 0.75 >0.75 – 1.00 >1.00 – 1.50

>1.50

1.5 2.0 2.5 3.0 3.5 4.0

1.5 2.0 2.5 3.0 3.5 3.5

1.5 2.0 2.0 2.5 3.0 3.0

1.5 2.0 2.0 2.5 3.0 3.0

1.5 2.0 2.0 2.5 3.0 3.0

1.5 2.0 2.0 2.5 3.0 3.0

1.5 1.5 2.0 2.0 2.5 2.5

1.5 1.5 2.0 2.0 2.5 2.5

1.5 1.5 2.0 2.0 2.5 2.5

>4 – 5

0.00 – 0.25 >0.25 – 0.50 >0.50 – 0.75 >0.75 – 1.00

>1.00

1.5 3.0 3.5 4.0 5.0

1.5 2.5 3.0 3.5 4.0

1.5 2.5 3.0 3.5 4.0

1.5 2.5 3.0 3.5 4.0

1.5 2.0 2.5 3.0 3.5

1.5 2.0 2.5 3.0 3.5

1.5 2.0 2.5 3.0 3.0

1.5 2.0 2.5 3.0 3.0

1.5 2.0 2.5 3.0 3.0

>5 – 6

0.00 – 0.25 >0.25 – 0.30 >0.30 – 0.50 >0.50 – 0.75 >0.75 – 1.00

>1.00

2.0 4.0 4.5 5.0 5.5 6.0

2.0 3.0 4.0 4.5 5.0 5.0

1.5 2.5 3.5 4.0 4.5 5.0

1.5 2.5 3.0 3.5 4.0 4.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

1.5 2.0 2.5 3.0 3.0 3.5

>6

0.00 – 0.25 >0.25 – 0.30 >0.30 – 0.50 >0.50 – 0.75 >0.75 – 1.00

>1.00

4.0 4.5 5.0 5.5 6.0 7.0

3.0 4.0 4.5 5.0 5.5 6.0

2.5 3.5 4.0 4.5 5.0 5.5

2.5 3.5 4.0 4.5 5.0 5.5

2.5 3.5 3.5 4.0 4.5 5.0

2.5 3.0 3.0 3.5 4.0 4.5

2.0 2.5 2.5 3.0 3.5 4.0

2.0 2.5 2.5 3.0 3.5 4.0

2.0 2.5 2.5 3.0 3.5 4.0

Note: Interpolation for percentage of trucks and buses is recommended to the nearest 0.1.

Percent Upgrade

Length (mi)

Proportion of RVs 2% 4% 5% 6% 8% 10% 15% 20% 25%

≤2 All 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2

>2 – 3 0.00 – 0.50

>0.50 1.2 3.0

1.2 1.5

1.2 1.5

1.2 1.5

1.2 1.5

1.2 1.5

1.2 1.2

1.2 1.2

1.2 1.2

>3 – 4 0.00 – 0.25

>0.25 – 0.50 >0.50

1.2 2.5 3.0

1.2 2.5 2.5

1.2 2.0 2.5

1.2 2.0 2.5

1.2 2.0 2.0

1.2 2.0 2.0

1.2 1.5 2.0

1.2 1.5 1.5

1.2 1.5 1.5

>4 – 5 0.00 – 0.25

>0.25 – 0.50 > 0.50

2.5 4.0 4.5

2.0 3.0 3.5

2.0 3.0 3.0

2.0 3.0 3.0

1.5 2.5 3.0

1.5 2.5 2.5

1.5 2.0 2.5

1.5 2.0 2.0

1.5 2.0 2.0

>5 0.00 – 0.25

>0.25 – 0.50 >0.50

4.0 6.0 6.0

3.0 4.0 4.5

2.5 4.0 4.0

2.5 3.5 4.0

2.5 3.0 3.5

2.0 3.0 3.0

2.0 2.5 3.0

2.0 2.5 2.5

1.5 2.0 2.0

Note: Interpolation for percentage of RVs is recommended to the nearest 0.1.

The length of the grade is generally taken from a highway profile. It typically

includes the straight portion of the grade plus some portion of the vertical curves

at the beginning and end of the grade. It is recommended that 25% of the length

of the vertical curves at both ends of the grade be included in the length. Where

two consecutive upgrades are present, 50% of the length of the vertical curve

joining them is included in the length of each grade.

Exhibit 14-13 PCEs for Trucks and Buses

(ET) on Upgrades

Exhibit 14-14 PCEs for RVs (ER) on

Upgrades

The grade length should include 25% of the length of the vertical curves at the start and end of the grade.

With two consecutive upgrades, 50% of the length of the vertical curve joining them should be included.


Methodology Page 15-28 Chapter 15/Two-Lane Highways January 2012

ATSHVATSgdATS ffc ,,700,1

PTSFHVPTSFgdPTSF ffc ,,700,1

where

cdATS = capacity in the analysis direction under prevailing conditions based on

ATS (veh/h), and

cdPTSF = capacity in the analysis direction under prevailing conditions based on

PTSF (veh/h).

For Class I highways, both capacities must be computed. The lower value

represents capacity. For Class II highways, only the PTSF-based capacity is

computed. For Class III highways, only the ATS-based capacity is computed.

One complication is that the adjustment factors depend on the demand flow

rate (in vehicles per hour). Thus, adjustment factors for a base flow rate of 1,700

pc/h must be used. Technically, this value should be adjusted to reflect grade and

heavy vehicle adjustments. This would create an iterative process in which a

result is guessed and then checked.

In practical terms, this is unnecessary, since the highest flow group in all

adjustment exhibits is greater than 900 veh/h. It is highly unlikely that any

adjustments would reduce 1,700 pc/h to less than 900 veh/h. Therefore, in

capacity determinations, all adjustment factors should be based on a flow rate

greater than 900 veh/h.

Another characteristic of this methodology must be considered in evaluating

capacity. When the directional distribution is other than 50/50 (in level and

rolling terrain), the two-way capacity implied by each directional capacity may

be different. Moreover, the implied two-way capacity from either or both

directions may be more than the limit of 3,200 pc/h. In such cases, the directional

capacities estimated are not achievable with the stated directional distribution. If

this is the case, then base capacity is restricted to 1,700 pc/h in the direction with

the heaviest flow, and capacity in the opposing direction is found by using the

opposing proportion of flow, with an upper limit of 1,500 pc/h.

Directional Segments with Passing Lanes

Providing a passing lane on a two-lane highway in level or rolling terrain

improves operational performance and therefore may improve LOS. A

procedure to estimate this effect is described in this section.

This procedure should be applied only in level and rolling terrain. On

specific grades, added lanes are considered to be climbing lanes, which are

addressed in the next section.

Exhibit 15-22 illustrates the operational effect of a passing lane on PTSF. It

shows that the passing lane provides operational benefits for some distance

downstream before PTSF returns to its former level (without a passing lane).

Thus, a passing lane’s effective length is greater than its actual length.

Equation 15-12

Equation 15-13

Capacity may be limited by the directional distribution of traffic and the total two-way base capacity of 3,200 pc/h.

The effective length of a passing lane is longer than its actual length.


Methodology Page 15-38 Chapter 15/Two-Lane Highways January 2012

WOL = outside lane width (ft),

Ws = paved shoulder width (ft),

V = hourly directional volume per lane (veh/h),

We = average effective width of the outside through lane (ft), and

%OHP = percentage of segment with occupied on-highway parking (decimal).

Step 4: Calculate the Effective Speed Factor

The effect of motor vehicle speed on bicycle quality of service is primarily

related to the differential between motor vehicle and bicycle travel speeds. For

instance, a typical cyclist may travel in the range of 15 mi/h. An increase in motor

vehicle speeds from 20 to 25 mi/h is more readily perceived than a speed increase

from 60 to 65 mi/h, since the speed differential increases by 100% in the first

instance compared with only 11% in the latter. Equation 15-30 shows the

calculation of the effective speed factor that accounts for this diminishing effect.

8103.0)20ln(1199.1 pt SS

where

St = effective speed factor, and

Sp = posted speed limit (mi/h).

Step 5: Determine the LOS

With the results of Steps 1–4, the bicycle LOS score can be calculated from

Equation 15-31:

057.0)(005.0)/1(066.7

)38.101(1999.0)ln(507.022

2

e

tOL

WP

HVSvBLOS

where

BLOS = bicycle level of service score;

vOL = directional demand flow rate in the outside lane (veh/h);

HV = percentage of heavy vehicles (decimal); if V < 200 veh/h, then HV

should be limited to a maximum of 50%;

P = FHWA’s 5-point pavement surface condition rating; and

We = average effective width of the outside through lane (ft).

Finally, the BLOS score value is used in Exhibit 15-4 to determine the bicycle

LOS for the segment.

Equation 15-30

Equation 15-31


Example Problems Page 15-44 Chapter 15/Two-Lane Highways January 2012

4. EXAMPLE PROBLEMS

Problem Number Description Type of Analysis

1 2 3 4 5

Find the LOS of a Class I highway in rolling terrain Find the LOS of a Class II highway in rolling terrain Find the LOS of a Class III highway in level terrain Find the LOS of a Class I highway with a passing lane Find the future bicycle LOS of a two-lane highway

Operational analysis Operational analysis Operational analysis Operational analysis Planning analysis

EXAMPLE PROBLEM 1: CLASS I HIGHWAY LOS

The Facts

A segment of Class I two-lane highway has the following known

characteristics:

Demand volume = 1,600 veh/h (total in both directions)

Directional split (during analysis period) = 50/50

PHF = 0.95

50% no-passing zones in the analysis segment (both directions)

Rolling terrain

14% trucks; 4% RVs

11-ft lane widths

4-ft usable shoulders

20 access points/mi

60-mi/h BFFS

10-mi segment length

Find the expected LOS in each direction on the two-lane highway segment as

described.

Comments

The problem statement calls for finding the LOS in each direction on a

segment in rolling terrain. Because the directional split is 50/50, the solution in

one direction will be the same as the solution in the other direction, so only one

operational analysis needs to be conducted. The result will apply equally to each

direction.

Because this is a Class I highway, both ATS and PTSF must be estimated to

determine the expected LOS.

Step 1: Input Data

All input data were specified above.

Step 2: Estimate the FFS

FFS is estimated with Equation 15-2 and adjustment factors found in Exhibit

15-7 (for lane and shoulder width) and Exhibit 15-8 (for access points in both

directions). For 11-ft lane widths and 4-ft usable shoulders, the adjustment factor

Exhibit 15-31 List of Example Problems


Chapter 19/Two-Way STOP-Controlled Intersections Page 19-15 Methodology January 2012

Step 4: Determine Critical Headways and Follow-Up Headways

The critical headways tc,x and follow-up headways tf,x must be determined for

the major-street left turns (vc,1 and vc,4), the minor-street right turns (vc,9 and vc,12),

the major-street U-turns (vc,1U and vc,4U), the minor-street through movements (vc,8

and vc,11), and the minor-street left turns (vc,7 and vc,10) as they occur at a TWSC

intersection.

To compute the critical headways for each movement, the analyst begins

with the base critical headway given in Exhibit 19-10 and makes movement-

specific adjustments relating to the percentage of heavy vehicles, the grade

encountered, and a three-leg versus four-leg intersection, as shown in Equation

19-30:

LTGcHVHVcbasecxc tGtPttt ,3,,,,

where

tc,x = critical headway for movement x (s);

tc,base = base critical headway from Exhibit 19-10 (s);

tc,HV = adjustment factor for heavy vehicles (1.0 for major streets with one

lane in each direction; 2.0 for major streets with two or three lanes in

each direction) (s);

PHV = proportion of heavy vehicles for movement (expressed as a decimal;

e.g., PHV = 0.02 for 2% heavy vehicles);

tc,G = adjustment factor for grade (0.1 for Movements 9 and 12; 0.2 for

Movements 7, 8, 10, and 11) (s);

G = percent grade (expressed as an integer; e.g., G = −2 for a 2% downhill

grade); and

t3,LT = adjustment factor for intersection geometry (0.7 for minor-street left-

turn movement at three-leg intersections; 0.0 otherwise) (s).

Base Critical Headway, tc,base (s) Vehicle Movement Two Lanes Four Lanes Six Lanes

Left turn from major 4.1 4.1 5.3

U-turn from major N/A 6.4 (wide)

6.9 (narrow) 5.6

Right turn from minor 6.2 6.9 7.1

Through traffic on minor 1-stage: 6.5

2-stage, Stage I: 5.5 2-stage, Stage II: 5.5

1-stage:6.5 2-stage, Stage I: 5.5 2-stage, Stage II: 5.5

1-stage: 6.5* 2-stage, Stage I: 5.5* 2-stage, Stage II: 5.5*

Left turn from minor 1-stage: 7.1

2-stage, Stage I: 6.1 2-stage, Stage II: 6.1

1-stage: 7.5 2-stage, Stage I: 6.5 2-stage, Stage II: 6.5

1-stage: 6.4 2-stage, Stage I: 7.3 2-stage, Stage II: 6.7

* Use caution; values estimated.

Note: “Narrow” U-turns have a median nose width < 21 ft; “wide” U-turns have a median nose width ≥21 ft.

The critical headway data for four- and six-lane sites account for the actual

lane distribution of traffic flows measured at each site. For six-lane sites, minor-

street left turns were commonly observed beginning their movement while

apparently conflicting vehicles in the far-side major-street through stream pass.

The values for critical headway for minor-street through movements at six-lane

streets are estimated, as the movement is not frequently observed in the field.

Equation 19-30

t3,LT is applicable to Movements 7, 8, 10, and 11

Exhibit 19-10 Base Critical Headways for TWSC Intersections


Methodology Page 19-16 Chapter 19/Two-Way STOP-Controlled Intersections January 2012

Similar to the computation of critical headways, the analyst begins the

computation of follow-up headways with the base follow-up headways given in

Exhibit 19-11. The analyst then makes movement-specific adjustments to the base

follow-up headways with information gathered on heavy vehicles and the

geometrics of the major street per the adjustment factors given in Equation 19-31.

HVHVfbasefxf Pttt ,,,

where

tf,x = follow-up headway for movement x (s),

tf,base = base follow-up headway from Exhibit 19-11 (s),

tf,HV = adjustment factor for heavy vehicles (0.9 for major streets with one

lane in each direction, 1.0 for major streets with two or three lanes in

each direction), and

PHV = proportion of heavy vehicles for movement (expressed as a decimal;

e.g., PHV = 0.02 for 2% heavy vehicles).

Base Follow-Up Headway, tf,base (s) Vehicle Movement Two Lanes Four Lanes Six Lanes

Left turn from major 2.2 2.2 3.1

U-turn from major N/A 2.5 (wide)

3.1 (narrow) 2.3

Right turn from minor 3.3 3.3 3.9 Through traffic on minor 4.0 4.0 4.0 Left turn from minor 3.5 3.5 3.8

Note: “Narrow” U-turns have a median nose width < 21 ft; “wide” U-turns have a median nose width ≥21 ft.

Values from Exhibit 19-10 and Exhibit 19-11 are based on studies throughout

the United States and are representative of a broad range of conditions. If smaller

values for tc and tf are observed, capacity will be increased. If larger values for tc

and tf are used, capacity will be decreased.

Step 5: Compute Potential Capacities

Step 5a: Potential Capacity If No Upstream Signal Effects Are Present

The potential capacity cp,x of a movement is computed according to the gap-

acceptance model provided in Equation 19-32 (6). This model requires the

analyst to input the conflicting flow rate vc,x, the critical headway tc,x, and the

follow-up headway tf,x, for movement x.

600,3/

600,3/

,, ,,

,,

1 xfxc

xcxc

tv

tv

xcxpe

evc

where

cp,x = potential capacity of movement x (veh/h),

vc,x = conflicting flow rate for movement x (veh/h),

tc,x = critical headway for minor movement x (s), and

tf,x = follow-up headway for minor movement x (s).

Equation 19-31

Exhibit 19-11 Base Follow-Up Headways

for TWSC Intersections

Equation 19-32


Chapter 20/All-Way STOP-Controlled Intersections Page 20-15 Methodology July 2012

Base Saturation Headway (s)

Case No. of Veh.

Group 1

Group 2

Group 3a

Group 3b

Group 4a

Group 4b

Group 5

Group 6

1 0 3.9 3.9 4.0 4.3 4.0 4.5 4.5 4.5

2 1 2 ≥3

4.7 4.7 4.8 5.1 4.8 5.3 5.0 6.2

6.0 6.8 7.4

3 1 2 ≥3

5.8 5.8 5.9 6.2 5.9 6.4 6.4 7.2

6.6 7.3 7.8

4

2 3 4 ≥5

7.0 7.0 7.1 7.4 7.1 7.6 7.6 7.8 9.0

8.1 8.7 9.6 12.3

5

3 4 5 ≥6

9.6 9.6 9.7 10.0 9.7 10.2 9.7 9.7 10.0 11.5

10.0 11.1 11.4 13.3

Step 10: Compute Departure Headways

The departure headway of the lane is the expected value of the saturation

headway distribution, given by Equation 20-28.

64

1isid hiPh

where i represents each combination of the five degree-of-conflict cases and hsi is

the saturation headway for that combination.

Step 11: Check for Convergence

The calculated values of hd are checked against the initial values assumed for

hd. If the values change by more than 0.1 s (or a more precise measure of

convergence), Steps 5 through 10 are repeated until the values of departure

headway for each lane do not change significantly.

Step 12: Compute Capacity

The capacity of each lane in a subject approach is computed under the

assumption that the flows on the opposing and conflicting approaches are

constant. The given flow rate on the subject lane is increased and the departure

headways are computed for each lane on each approach until the degree of

utilization for the subject lane reaches 1. When this occurs, the final value of the

subject lane flow rate is the maximum possible throughput or capacity of this

lane.

Step 13: Compute Service Times

The service time required to calculate control delay is computed on the basis

of the final calculated departure headway and the move-up time with Equation

20-29.

mht ds

where ts is the service time, hd is the departure headway, and m is the move-up

time (2.0 s for Geometry Groups 1 through 4; 2.3 s for Geometry Groups 5 and 6).

Equation 20-28

Capacity is estimated for a stated set of opposing and conflicting volumes.

Equation 20-29


Chapter 20/All-Way STOP-Controlled Intersections Page 20-25 Example Problem July 2012

0004.06)088.0(3)0(2)052.0(01.0)5( AdjP

0001.027)052.0(6001.0 )16( AdjP

Therefore, the adjusted probability for Combination 1, for example, is as

follows:

5445.00065.0538.0)1(' P

Step 9: Compute Saturation Headways

The base saturation headways for each combination can be determined with

Exhibit 20-14. They are adjusted by using the adjustment factors calculated in

Step 4 and added to the base saturation headways to determine saturation

headways as follows (eastbound illustrated):

i hbase hadj hsi

1 3.9 0.063 3.963

2 4.7 0.063 4.763

5 5.8 0.063 5.863

7 7.0 0.063 7.063

Step 10: Compute Departure Headways

The departure headway of the lane is the sum of the products of the adjusted

probabilities and the saturation headways as follows (eastbound illustrated):

57.4)063.7)(0524.0()863.5)(0875.0()763.4)(3213.0()963.3)(5445.0( dh

Step 11: Check for Convergence

The calculated values of hd are checked against the initial values assumed for

hd. After one iteration, each calculated headway differs from the initial value by

more than 0.1 s. Therefore, the new calculated headway values are used as initial

values in a second iteration. For this problem, four iterations are required for

convergence.

EB EB WB WB NB NB SB SB

L1 L2 L1 L2 L1 L2 L1 L2

Total Lane Flow Rate 368 421 158

hd, initial value, iteration 1 3.2 3.2 3.2

x, initial, iteration 1 0.327 0.374 0.140

hd, computed value, iteration 1 4.57 4.35 5.14

Convergence? N N N




Convergence? N N N




Convergence? Y Y N




Convergence? Y Y Y


Example Problem Page 20-26 Chapter 20/All-Way STOP-Controlled Intersections July 2012

Step 12: Compute Capacity

The capacity of each lane in a subject approach is computed by increasing the

given flow rate on the subject lane (assuming the flows on the opposing and

conflicting approaches are constant) until the degree of utilization for the subject

lane reaches 1. This level of calculation requires running an iterative procedure

many times, which is practical for a spreadsheet or software implementation.

Here, the eastbound lane capacity is approximately 720 veh/h, which is lower

than the value that could be estimated by dividing the lane volume by the degree

of utilization (368/0.492 = 748 veh/h). The difference is due to the interaction

effects among the approaches: increases in eastbound traffic volume increase the

departure headways of the lanes on the other approaches, which in turn

increases the departure headway of the lane(s) on the subject approach.

Step 13: Compute Service Times

The service time required to calculate control delay is computed on the basis

of the final calculated departure headway and the move-up time by using

Equation 20-29. For the eastbound lane (using a value for m of 2.0 for Geometry

Group 1), the calculation is as follows:

97.20.297.4 mht ds

Step 14: Compute Control Delay

The control delay for each lane is computed with Equation 20-30 as follows

(eastbound illustrated):

s 0.135)25.0(450

)508.0(97.41508.01508.0)25.0(90097.2 2

d

By using Exhibit 20-2, the eastbound lane (and thus approach) is assigned

LOS B. A similar calculation for the westbound and southbound lanes (and thus

approaches) yields 13.5 and 10.6 s, respectively.

The control delays for the approaches can be combined into an intersection

control delay by using a weighted average as follows:

s 8.12158421368

)158)(6.10()421)(5.13()368)(0.13(

d

This value of delay is assigned LOS B.

Step 15: Compute Queue Length

The 95th percentile queue for each lane is computed with Equation 20-33 as

follows (eastbound approach illustrated):

veh 9.2

25.0150

508.097.41508.01508.0

97.4

25.0900 295

Q

This queue length would be reported as 3 vehicles.

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